IJESRT /Archives-2015/June-2015/67...In the present work a shell and tube heat exchanger is modeled...

[Jain, 4(6): June, 2015] ISSN: 2277-9655

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IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH

TECHNOLOGY COMPARATIVE STUDY OF DIFFERENT CFD MODELS TO EVALUATE HEAT

TRANSFER AND FLOW PARAMETERS IN STHE

Anshul Jain*, Prof. K. K. Jain, Prof. Sudarshan Patel

(*ME student, Prof. & Head, Prof. SRIT, Jabalpur) * Mechanical Engineering Department, SRIT Jabalpur, India

ABSTRACT Computational fluid dynamics ( CFD) simulations can be very useful to investigate heat transfer and visualize the

temperature fields & fluid flow characteristics of shell and tube heat exchanger. A shell and tube heat exchanger is

modeled to find the heat transfer parameters. The heat exchanger contains tubes inside with baffle arrangement. The

flow and temperature fields are resolved using CFD package (ANSYS FLUENT). The experimental investigation

has been also performed for comparison purpose. The CFD turbulence models considered for investigation are k-

epsilon, SST, Eddy Viscosity and Laminar model. Laminar flow is consider for understanding the significance of

turbulence in the flow field. The boundary conditions taken for the computational domain are derived out of the

experimental investigation results. Transient analysis has been performed for the physical time scale of 1800

seconds. Unstructured meshing method is used to create mesh on the domain. It has been find out that k-epsilon

model came out to be the best model to predict the flow parameters, heat transfer coefficient and behavior of present

case of STHE.Reasonable agreement is found between the simulation and experimental data.

KEYWORDS: Shell & tube; Turbulence ; CFD; heat transfer parameters.

INTRODUCTION Heat exchangers are one of the most important heat transfer apparatus that are used in industries like

chemical engineering, oil refining, electric power generation etc. Shell-and-tube types of heat exchangers

(STHXs) have been commonly and most effectively used in Industries over the years. The shell-and-tube heat

exchangers are still the most common type in use. They have larger heat transfer surface area-to-volume ratios than

the most of common types of heat exchangers, and they are manufactured easily for a large variety of sizes

and flow configurations. They can operate at high pressures, and their construction facilitates disassembly for

periodic maintenance and cleaning. The shell-and-tube heat exchangers consist of a bundle of tubes enclosed

within a cylindrical shell. One fluid flows through the tubes and a second fluid flows within the space between

the tubes and the shell. Typical Shell-and-Tube heat exchanger is shown in Figure 1.1.

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Its unavoidable need has necessitated work on efficient and reliable designs leading towards optimum share in the

overall system performance. The Log Mean Temperature Difference (LMTD) method and the number of heat

transfer units (NTU) method have been used for heat exchanger design . These methods have some shortcomings

associated with them i.e. iterative in nature and need of a prototype to implement the design. Due to these reasons,

these methods are time consuming as well as expensive especially for large scale models. However, economical

access to powerful micro processors has paved the way for evolvement of Computational Fluid Dynamics (CFD)

during the design phase.( V. Kumar, S. Saini et al 2006)

CFD is a science that can be helpful for studying fluid flow, heat transfer, chemical reactions etc by solving

mathematical equations with the help of numerical analysis. It is equally helpful in designing a heat exchanger

system from troubleshooting and optimization by suggesting design modifications.

CFD employs a very simple principle of resolving the entire system in small cells or grids and applying governing

equations on these discrete elements to find numerical solutions regarding pressure distribution, temperature

gradients, flow parameters and the like in a shorter time at a lower cost because of reduced required experimental

work (Y. Wang, Q. Dong, M. Liu et al 2007)

In the present work a shell and tube heat exchanger is modeled to investigate the heat transfer parameters. The heat

exchanger contained 14tubes inside a 1025 mm long and 156 mm diameter shell with baffle arrangement. The flow

and temperature field inside the shell and tube are resolved using CFD package (ANSYS CFX 13.0). A set of CFD

simulations is performed for a single shell and tube bundle and is compared with experimental results.

The four CFD models are considered and are compared to find the best suitable model for the present case. The

modeling has been done in design modular module in the Ansys package. The meshing has been done using un-

structural Tetrahedral mesh element. And the mesh of the element fixed after grid dependency test has been found to

be 779491 elements. (ref. Appendix.A)

The results are found to be good for the turbulence model. Further the k-epsilon model predict the flow parameters

and heat transfer-coefficient more accurately then other models.

COMPUTATIONAL MODELLING

The first step of computational modeling is Geometry Modeling. It requires the geometric parameters of

the model. It is a mathematical model that requires extensive computational resources to study the

behavior of complex system by computer simulation. Instead of deriving the analytical solution of the

problem by solving complex mathematical equations, experimentation with the model is done by setting

the parameters of the system in the computer.CFD resolves the entire system in small cells and apply the

governing equations to find numerical solutions with regard to fluid flow and temperature distribution. It

creates a virtual prototypes of the system and gives the numerical solution in a shorter time and lower cost

due to reduced required experimental work. The basic approach of usind CFD are

(A)Pre-processor (B) solver (C) Post-processor.

GOVERNING EQUATIONS

The flow is governed by the continuity equation, the energy equation and Navier-Stokes momentum

equations. Transport of mass, energy and momentum occur through convective flow and diffusion of

molecules and turbulent eddies. All equations are set up over a control volume where i, j, k = 1, 2, 3

correspond to the three dimensions.

Continuity Equation

The continuity equation describes the conservation of mass and is written as in equation


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(b)Momentum Equations (Navier- Strokes Equations )

( c ) Energy Equation

Turbulence Model :

Since the flow in this study is turbulent, so turbulence effect should be considered using turbulence

modeling. The choice of turbulence is very critical in CFD simulations. However, there is no universal

criterion for selecting a turbulence model. On the basis of literature available, and for comparing the

performance of the turbulence model; three turbulence model are consider in this study. One laminar

model is also consider to understand the effects of turbulence. In this study k − ε turbulence model, k − ω

SST model, Eddy-viscosity model and laminar viscosity model are considered.

( i ) k − ε Model : The first transported variable is turbulent kinetic energy, k. The second transported

variable in this case is the turbulent dissipation, ε. There respective modeled transport equations are as

under

For k,

And for ε

The closure coefficients for k – ε models are Cµ =0.09 , Cε1 = 1.44, Cε2 = 1.92 , σk =1.00 , σε = 1.34

The physical interpretation of the ε equation is,

1. Accumulation of ε 2. Convection of ε by the mean velocity 3. Production of ε

4. Dissipation of ε 5. Diffusion of ε

(ii) k − ω SST Model- It has been a problem to accurately predict the flow separation. The modeled

equation for k is as under

and the modeled equation for ω is

Closure Coefficients for k − ω Model are α = 5/9, β= 3/40, β∗ σk= ½ , σω = ½


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(iii) Eddy-Viscosity Model : The concept behind the eddy-viscosity model are that the unknown

Reynolds stresses, a consequence from the averaging procedure, are modeled using flow parameters

(strain rate tensor & rotation tensor) and an eddy viscosity

( iv ) Laminar viscosity model : The laminar viscosity model is used for specifying the viscous

conditions of flow. It defines the laminar flow, it is based on Navier strokes equation

METHODOLOGY AND EXPERIMENTAL WORK

Methodology:

EXPERIMENT ON THE SETUP TO COLLECT READING FOR B.COND.

SELECTION OF PARAMETERS(temp, velocity etc )

MODELING OF EXPERIMENTAL SETUP IN CAD

DESCRITIZATION OF CAD MODEL

DEFINING BOUNDARY CONDITION

SELECTION OF PHYSICAL MODEL FOR PROBLEM

ANALYSIS OF STHE BY SELECTED FOUR MODELS

POST PROCESSING THE RESULTS

COMPARING THE RESULTS AND CONCLUSION


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Experimental setup description :

The Experimental observations are as follows

1. Steam pressure (gauge) (kg/cm2) = 0.25 (kg/cm2) =0.245 bar

2. Water inlet temperature = 29.5oC.

3. Water outlet temperature = 72.4oC.

4. Water flow rate = 11.5 cc/sec.

5. Steam inlet temperature = 102.1oC.

6. Steam Outlet temperature = 81.2oC.

7. Condensate volume collected = 340 ml.

8. Time of collection = 60 sec.

RESULTS AND DISCUSSION

Figure 1,2,3,4 represents the results obtained by eddy viscosity model, k-epsilon model,laminar model

and shear stress transport(SST) model respectively.

1. Logarithmic temperature distribution of heat exchanger pipe along the length.

HEAT EXCHANGER DIMENSIONS

No. Description Unit Value

1 Shell outside diameter mm 156

2 Shell inside diameter mm 150

3 Tube outer diameter mm 12

4 Tube inner diameter mm 10

5 Number of tubes 14

6 Shell/Tube length mm 1025

7 Number of baffles mm 4

8

.

Baffle spacing

mm 205

9

.

Baffle inclination 0o


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Comments :

Eddy Viscosity model and Shear stress transportation model generated the unsatisfactory results due to

violation of exit temperature criterion. Laminar viscosity model generated the realistic results but due to

turbulences encountered in steam and water particle practically this results are also not giving the

satisfactory correlation with experimental results. So the best suited criterion for this heat exchanger

problem solving is K-Epsilon model. So the best suited criterion for heat exchanger problem solving is K-

Epsilon model. Results are matched and validated by the experimental results, because this model having

a fear balance between the turbulence and shear at wall.

2 . Heat transfer coefficient of heat exchanger pipe along the length.

Comments :

Eddy Viscosity model and Shear stress transportation model generated the unsatisfactory results due to

dominancy of the turbulences criterion consideration by these two models. So the heat transfer coefficient

is vulnerable throughout the flow. In Laminar viscosity model the flow is stable and free from eddy but

not a practical case. Results are also not giving the satisfactory correlation with experimental results.So

for the mix flow (steam and water) problems of heat transfer the K-Epsilon model gives the best results

that is because, this model having a fear balance between the turbulence and shear at wall for moderate

fluid flow conditions.


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3. Steam Temperature distribution of heat exchanger pipe.

Comments: Steam Temperature distributions inside the casing of heat exchanger are shown in the

figures. The high heat transfer zones or where the turbulence involves the temperature of the steam

reduces abruptly. This abrupt behavior is undesirable, so as the K-epsilon model shows the minimum

inconsistency across the flow line.

4.Sectional view of water temperature distribution of heat exchanger pipe.


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5.Heat transfer coefficient distribution of heat exchanger pipe.

Comment :There is a pictorial representation of Heat Transfer coefficient among the all models. K-

epsilon model represent the consistent pattern of heat transfer coefficient whereas laminar. Eddy and SST

models are non-uniform and random heat transfer coefficient generators. So for the low and moderate

velocity force convective systems like our case, the K-ε Viscosity model is best suited.

6. Steam line for stream distribution of heat exchanger pipe.


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Comments: Vortecity is generated due to shear or velocity gradient among the particle and also due to

wall and fluid interface but the major role of vortex comes into the picture when the turbulent fluid

interact with baffles inside the tubes. Eddy viscosity, laminar and SST model are not able to generate the

ideal condition for problem solving, due to over-dominancy of turbulence in Eddy and SST model.

Results are best fit for K-epsilon model. So for the general purpose discreet fluid interaction problems are

solving by this particular method.

COMPARISION OF RESULTS AND DISCUSSION :

(a)Comparison of Results of Different CFD models with Experimental Results

Sr.

No Parameter

Experimental

Result

Eddy

Viscosity

Model

Laminar

viscosity

Model

k-ε

Model

Shear Stress

Transport

Model

1 Steam Inlet Temperature (°C) 102.1 102.1 102.1 102.1 102.1

2 Steam Outlet Temperature (°C) 81.2 82.8 79.1 83.2 89.9

3 Water Inlet Temperature (°C) 29.5 29.5 29.5 29.5 29.5

4 Water outlet Temperature (°C) 72.4 99.1 57.1 69.9 86.3

5 Water Wall side CHT (W/m2K) 117.072 1407 133.5 143.5 391.5

6 Steam Wall side CHT (W/m2K) 235.180 951.1 79.93 297.24 322.8

Table 5.1: Comparative study of results.

(b)Comparison of Water Outlet temperature.

The Water outlet temperature is more accurately predicted by k-ε model than the other CFD model

considered. The outlet temperature of water predicted by k-ε model has a difference of 2.5 oC or 3.5 %

with the experimental results, while the other models show greater variation. So a good agreement is

shown between experimental and simulation result by k-ε model.

Figure: Water outlet temperature graph.


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( c )Comparision of Steam outlet temperature.

The outlet temperature of steam obtained by the considered CFD models shows a close agreement with

the experimental results except for the case of shear stress transport model which over predict the result

by 10% while the other models predict the result by ±2.5%. Moreover the Eddy viscosity model and k-ε

model shows a close agreement with the experimental results. The k-ε model predict the steam outlet

temperature with the difference of 2oC or less than 2.5%.So a good agreement is shown between

experimental and simulation result by k-ε model.

Figure: Steam outlet temperature graph.

(d) Comparison of Water wall side heat transfer coefficient.

The Water wall side heat transfer coefficient obtained by the experiment and the considered CFD models

are shown in following graph. The water wall side CHT predict by Eddy Viscosity model is much higher

than the experimental value, which is not feasible at all. Also the SST model over predict the CHT with a

large difference.The laminar viscosity and k-ε model shows a fair good agreement with the experimental

value of water wall side heat transfer coefficient.But the Pictorial representation of heat transfer

coefficient by the laminar viscosity model is non uniform and it generates random heat transfer

coefficient, while the k-ε model represent consistent pattern of heat transfer coefficient, so for the low

and moderate velocity force convective system in the present case, k-ε viscosity model is best suited.

Figure: Water wall side CHT graph


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( e ) Steam Wall side heat transfer coefficient- comment.

The steam wall side heat transfer coefficient obtained by the experiment and the considered CFD models

are shown in following graph. The eddy viscosity model over predict the steam side CHT by a much

higher value than experimental result, so it is not feasible at all. More over the laminar viscosity model

under predict the steam side CHT also the laminar viscosity model is not applicable at all in such case.

The k-ε model shows a fair good agreement with the experimental value of steam side CHT. So for such

type of models k-ε model is best suited.

Figure : Steam wall side CHT graph

CONCLUSION During the CFD analysis it has been found out that laminar model totally failed to predict the flow parameters as

well as CHT parameters. And the other entire turbulence model shows significant improvement over laminar model.

Out of three turbulence model, the SST model is over predicting the turbulence & separation due to which the

thermal aspects of the flow shows the higher value. And the same happens with the eddy viscosity model, which

predicts the high eddy formation in the baffle section which leads to the higher steam side CHT as well as water side

which is not feasible at all. Further the K-epsilon is predicting the behavior moderately. It predicts the Water side

heat transfer coefficient as well as Steam side heat transfer coefficient more closely to the experimental values. It

also predict the flow parameters, water outlet temperature, steam outlet temperature more closely to the

experimental results. It shows good agreement with the literature available on the use of k-epsilon model.

NOMENCLATURE

A = Heat transfer area (m2

)

hm = Kine t ic E ner gy

hT = Thermal Energy

hC = Chemical Energy

h = Total energy

hh = Hot side heat transfer coefficient (W/m2.K )

hc = Cold side heat transfer coefficient (W/m2

.K )

K = Exchanger wall material thermal conductivity (W/m.K )

Q = Heat transfer rate (W)

Rf = Fouling coefficient (W/m2

.K )

T = Temperature (K)

t = Time (s)

U = Overall heat transfer coefficient (W/m2

.K )

u =Velocity (m/s)

v =Fluid flow velocity (m/s)


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V =Volume (m3)

∆TLM

=Logarithmic mean temperature difference (K)

∆x = Exchanger tube wall thickness (m)

Φ = Potential Energy

k= turbulence kinetic energy

ε = turbulence dissipation rate.

ω = specific dissipation rate

τ = time constant for turbulence.

Cµ , Cε1, Cε2, σk , σε = Closure Coefficients for k − ε Model.

α, β, β∗ σk, σω = Closure Coefficients for k − ω Model

µt = effective turbulent viscosity

ρ =Density (kg/m3)

x, y, z = Spatial coordinates (m)

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http://www.ansys.com/

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